If you wish to keep the two part associative and yet have each model have it's own part file, your only real solution is to use WAVE linking.
Once you've completed your Right-Hand Part, create an Assembly file and add the Right-Hand Part as a Component. Now create a second Component in the context of the assembly using...
Assemblies -> Components -> Create New...
...and when it asks you to
"Select objects to move or copy into the new component" do NOT make any selections but rather just hit OK and then assign the name that you wish to give the Left-Hand Part.
Now, while still in the Assembly file, make the new Component you have just added the Work Part. Now go to...
Insert -> Associative Copy -> WAVE Geometry Linker...
...and with the 'Type' set to 'Mirror Body', select the Right-Hand model and an appropriate Datum Plane (if you don't already have a Datum Plane in the Right-Hand Part you may wish to add one to the current Work Part as you will need one somewhere to complete the operation) and hit OK. Note that if you wish for ALL changes made to the Right-Hand Part, including any new features which might be added to it, to be copied over to the Left-Hand Part make sure that under the 'Settings' section of the WAVE dialog that the 'Fix at Current Timestamp' option is toggled OFF.
Now save the all the models and you set to go, at least as far as the models are concerned. Note that the Assembly that you created in order to perform the WAVE Linked copy operation, well that Assembly does not technically need to be kept since it had basically done its job, but you may wish to keep it since it does provide you with a better record of what you did even if it no longer plays a role in keeping the Left-Hand Part up-to-date with the Right-Hand Part.
Now as for your Drawings. If you are NOT using the Master Model approach, that is you created your drawing inside the Right-Hand Part and NOT as a separate Assembly file referencing the Right-Hand part file, you're are basically forced to start over and create from scratch a Drawing of the Left-Hand Part inside its Part file. However, if you HAD used the Master Model approach, while you will still need to do some additional work, it's not quite as bad. First open the original Drawing file for the Right-Hand Part, switch to Modeling and go to the Assembly Navigator and select the Component for the Right-Hand Part and press MB3 and select the 'Substitute' option. When it asks for the part file select your newly created Left-Hand Part file and accept all of the default options presented and and once the component has been replaces go the Drafting and display the Drawing. Now you will probably have to move the views around to get them to line up as you would like them and you will need to re-associate your dimensions which can be done by selecting a misplaced Dimension, pressing MB3 and selecting the 'Edit Associativity' option and then it will lead you through the steps needed to reattach the dimensions to the new edges and corners and such.
Anyway, that is the best approach which meets all of your criteria.
John R. Baker, P.E.
Product 'Evangelist'
Product Design Solutions
Siemens PLM Software Inc.
Cypress, CA
To an Engineer, the glass is twice as big as it needs to be.